The purpose of this task is to give students practice constructing functions …
The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.
The primary purpose of this task is to lead students to a …
The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.
The purpose of this task is to use finite geometric series to …
The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.
This short video and interactive assessment activity is designed to teach second …
This short video and interactive assessment activity is designed to teach second graders about capacity comparison problems with illustrations - word problems.
This short video and interactive assessment activity is designed to teach fourth …
This short video and interactive assessment activity is designed to teach fourth graders about finding the amount of water with illustrations and calculations (metric units).
The task requires the student to use logarithms to solve an exponential …
The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.
In the task "Carbon 14 Dating'' the amount of Carbon 14 in …
In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.
This problem introduces the method used by scientists to date certain organic …
This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.
This exploratory task requires the student to use a property of exponential …
This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.
In this task, students can see that if the price level increases …
In this task, students can see that if the price level increases and peopleŐs incomes do not increase, they arenŐt able to purchase as many goods and services; in other words, their purchasing power decreases.
In this video segment from Cyberchase, the CyberSquad and Digit construct a …
In this video segment from Cyberchase, the CyberSquad and Digit construct a physical profile of the person who kidnapped Choocroca, a giant cybercrocodile.
The goal of this class is to prove that category theory is …
The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.
In this Nrich activity students explore patterns with numbers in a square. …
In this Nrich activity students explore patterns with numbers in a square. This activity encourages multiple responses, creativity, discourse, and number sense.
This task presents a real-world problem requiring the students to write linear …
This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.
This simple task assesses whether students can interpret function notation. The four …
This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.
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